Mean Dynamics and Elevation‐Contributing Area Covariance in Landscape Evolution Models

Abstract

AbstractThe temporal dynamics of the land surface are commonly modeled by so‐called landscape evolution models, consisting of coupled partial differential equations accounting for the balance of sediment and water. An average sediment budget equation for a landscape evolution model in detachment‐limited condition is derived in terms of curvature‐dependent and curvature‐independent components. This highlights the role of plane curvature and spatial distribution of surface divergence/convergence on the average erosion rate. Performing a Reynolds‐type averaging of the original equations leads to a decomposition of the erosion into an unchannelized erosion sink and a channelization sediment flux. The latter is the derivative of a potential (referred to as “channelization sediment potential”) that arises from the negative correlation of elevation and specific drainage area and closely resembles, in both form and behavior, the Reynolds stress in fluid turbulence. The negative elevation‐area covariance emerges as a statistical signature of surface channelization. Building on analogies between landscape channelization and fluid turbulence, these theoretical results may provide a path to estimate model parameters from observations and offer useful benchmarks for numerical simulations in the channelized regime.